Table 5 Parameters

Time

T

\(\mathbb {N}\)

-

35040

number of time steps

M

\(\mathbb {N}\)

-

12

number of months

ts

\(\mathbb {R}_{+}^{T}\)

s

900¹

time steps

PV

N

\(\mathbb {N}\)

-

4

number of PV configurations

J

\(\mathbb {N}\)

-

4

number of roof planes

Cf^pv

\(\mathbb {R}_{+}\)

CHF

2749

PV fixed cost

C ^mod

\(\mathbb {R}_{+}^{N}\)

CHF/W

0.610¹

PV configurations, specific costs

\(P^{\textsc {mod}}_{\text {nom}}\)

\(\mathbb {R}_{+}^{N}\)

W

315¹

PV unit nominal power

P ^mod

\(\mathbb {R}_{+}^{T\times N}\)

W

²

PV configuration unit generation

A ^mod

\(\mathbb {R}_{+}^{N}\)

m²

1.631¹

PV configuration areas

A ^roof

\(\mathbb {R}_{+}^{J}\)

m²

23¹

roof planes areas

γ ^PV

\(\mathbb {R}\)

-

0.5%

annual maintenance specific cost

β _i

[0−90]^N

deg

³

ω _i

[0−360]^N

deg

³

PV configuration azimuth

Battery

B

\(\mathbb {N}\)

-

1

number of batteries

soc₀

[0,1]^B

-

0.7

initial state of charge

soc_min

[0,1]^B

-

0

minimum state of charge

soc_max

[0,1]^B

-

0.7

maximum state of charge

α

\(\mathbb {R}_{+}^{B}\)

s ⁻¹

4.63·10⁻⁷

battery self-discharge rate

η ^cha

[0,1]^B

-

0.98

battery charging efficiency

η ^dis

[0,1]^B

-

0.98

battery discharging efficiency

γ ^cha

\(\mathbb {R}_{+}^{B}\)

1/s

1/3600

battery charge C rate

γ ^dis

\(\mathbb {R}_{+}^{B}\)

1/s

1/3600

battery discharge C rate

C ^bat

\(\mathbb {R}_{+}^{B}\)

CHF/J

5.07·10⁻⁵⁴

battery specific cost

\(C_{F}^{\textsc {bat}}\)

\(\mathbb {R}_{+}^{B}\)

CHF

0

battery fixed cost

\(C_{O}^{\textsc {bat}}\)

\(\mathbb {R}_{+}^{B}\)

CHF/J

0

operational cost of storage

System

L

\(\mathbb {N}\)

years

25

system lifetime

L ^bat

\(\mathbb {R}_{+}\)

years

9

expected battery lifetime

r

\(\mathbb {R}\)

-

1.5%

discount rate